Step 1 :The z-score is a measure of how many standard deviations an element is from the mean.
Step 2 :If the z-score is zero, it means that the element is exactly at the mean.
Step 3 :Therefore, the corresponding x-value is equal to the mean.
Step 4 :The mean itself is not necessarily zero, and the x-value is not necessarily zero either. They are just equal to each other.
Step 5 :\(\boxed{\text{C. The corresponding $x$-value is equal to the mean, because the $z$-score is equal to the difference between the $x$-value and the mean, divided by the standard deviation.}}\)